A front-fixing finite element method for the valuation of American options with regime switching

Abstract

American option problems under regime-switching model are considered in this paper. The conjectures in [H. Yang, A numerical analysis of American options with regime switching, J. Sci. Comput. 44 (2010), pp. 69–91] about the position of early exercise prices are proved, which generalize the results in [F. Yi, American put option with regime-switching volatility (finite time horizon) – Variational inequality approach, Math. Methods. Appl. Sci. 31 (2008), pp. 1461–1477] by allowing the interest rates to be different in two states. A front-fixing finite element method for the free boundary problems is proposed and implemented. Its stability is established under reasonable assumptions. Numerical results are given to examine the rate of convergence of our method and compare it with the usual finite element method.

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